[Paper Review] The role of blood circulatory system in thermal regulation of animals explained by entropy production analysis

Michael Zakharov, Michael G. Sadovsky|arXiv (Cornell University)|Aug 16, 2013

Thermoregulation and physiological responses22 references3 citations

TL;DR

This paper proposes a non-equilibrium thermodynamic model of thermal regulation in homeothermic animals, using entropy production analysis to explain how blood circulation enables stable core temperature maintenance. It demonstrates that linear correlation between skin and environmental temperatures arises from entropy balance, with blood flow acting as a passive yet efficient heat transfer mechanism governed by the Second Law of Thermodynamics.

ABSTRACT

A novel model of thermal regulation of homoeothermic animals has been implemented. The model is based on a non-equilibrium thermodynamic approach which introduces entropy balance and the rate of entropy generation as a formulation of The Second Law. The model explains linear correlation between an animals skin and environment temperatures using the first principles and demonstrates the role of blood circulation in the thermoregulation of homoeothermic animals.

Motivation & Objective

• To develop a thermodynamically consistent model of thermal regulation in homeothermic animals based on non-equilibrium thermodynamics.
• To explain the observed linear correlation between skin temperature and environmental temperature using first principles.
• To clarify the functional role of blood circulation in heat dissipation, framing it as a consequence of entropy production minimization.
• To move beyond Newton’s cooling law by modeling active thermoregulation as a non-equilibrium steady-state process.
• To establish a foundation for modeling extreme physiological states such as sleep, hibernation, and torpor within a unified thermodynamic framework.

Proposed method

• Uses a 'core and shell' model to represent the animal body, with the core as a source of irreversible metabolic heat production.
• Applies the entropy balance equation and rate of entropy generation as a formulation of the Second Law to describe heat transfer.
• Models heat dissipation through the skin (shell) as a passive, steady-state process driven by thermal gradients.
• Assumes the core is a large, homogeneous, closed system in a non-equilibrium steady state with constant heat generation rate $ H_{\text{exc}} $.
• Treats the shell temperature $ T_s $ as determined by the Second Law rather than controlled directly, allowing local optimization of heat transfer.
• Introduces local control of core temperature $ T_c $ and heat flux $ J_c $, enabling spatially heterogeneous regulation without requiring uniform skin temperature.

Experimental results

Research questions

• RQ1 How can the linear correlation between skin temperature and environmental temperature in homeothermic animals be explained from first principles?
• RQ2 What is the thermodynamic role of blood circulation in maintaining stable core temperature despite environmental fluctuations?
• RQ3 Why is Newton’s cooling law inadequate for modeling active thermoregulation in living organisms?
• RQ4 How does the entropy production rate govern the efficiency and stability of heat dissipation in homeothermic animals?
• RQ5 Can the model be extended to describe physiological states such as sleep, hibernation, or torpor through distinct thermodynamic regimes?

Key findings

• The model explains the linear relationship between skin temperature and environmental temperature as a consequence of entropy production minimization in a non-equilibrium steady state.
• Blood circulation is shown to function as an optimal, passive heat transfer mechanism that emerges naturally from the Second Law, without requiring active control of skin temperature.
• The core temperature $ T_c $ and heat flux $ J_c $ can be locally optimized, while the shell finds a steady-state temperature $ T_s $ determined by the ambient conditions and entropy balance.
• The model demonstrates that excessive heat production in homeothermic animals is managed through a thermodynamically efficient, non-equilibrium process governed by entropy generation.
• The approach provides a theoretical basis for understanding thermal regulation beyond Newtonian cooling, showing that living systems actively resist thermal equilibrium.
• The framework is extendable to model diurnal rhythms and torpor states by switching between different metabolic regimes within the same thermodynamic formalism.